You don't have to put cheese in. The french version (pistou) is without pine nuts and cheese. Halfpint's recipe is pretty much the same thing. It will be just as good without the cheese albeit different.

If he misses the complexity of cheese, you could make one of these variations:
*with carrot tops (or greens)
*hazelnut oregano (good on squash ravioli)
*mint cumin (good on Moroccan dishes)
*walnut za'atar (good on bread or fish)
*Sicilian - with almond raisin caper anchovy pepperoncini (good on spiral pasta)

Have you thought about nutritional yeast? I use it when I'm out of parmesan or I'm being lazy. It's included in a lot of vegan pesto recipes - there's something about it that is very reminiscent of that salty, nutty bite of parmesan. Good luck!